Question: Simplify the following expression: $y = \dfrac{-54p - 90}{-90p - 117}$ You can assume $p \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-54p - 90 = - (2\cdot3\cdot3\cdot3 \cdot p) - (2\cdot3\cdot3\cdot5)$ The denominator can be factored: $-90p - 117 = - (2\cdot3\cdot3\cdot5 \cdot p) - (3\cdot3\cdot13)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $y = \dfrac{(9)(-6p - 10)}{(9)(-10p - 13)}$ Dividing both the numerator and denominator by $9$ gives: $y = \dfrac{-6p - 10}{-10p - 13}$